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IEEE International Conference on Networking, Sensing and Control (ICNSC)

Normalized Neural Network for Belief Propagation LDPC Decoding

Yiduo Tang, Lin Zhou, Shuying Zhang, Chen Chen, Lin Wang

Published Dec 3, 2021• 8 citations
Publisher

Abstract

BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.

DOI
10.1109/icnsc52481.2021.9702213

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BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.
For the Belief Propagation (BP) algorithm of low-density parity-check (LDPC) codes, existing deep learning methods have a limited performance improvement and it is difficult to train deep-level networks. In this paper, a model-driven quasi-residual network (Quasi-ResNet) BP decoding architecture is proposed for LDPC codes to further improve the performance of standard BP decoding. This method feeds the reliable messages calculated in current iteration into the next iteration based on the shortcut connection, and adjusts the weight of shortcut connection based on the error Back Propagation algorithm of neural network to determine the optimal genetic proportion of reliable messages. The decoding architecture is composed of a model-driven deep neural network (DNN) and shortcut connection. Simulation results show that the decoder can not only unfold more layers quickly compared with the DNN-based BP decoder, but also further improve the decoding performance.
We investigate the application of machine learning techniques (in particular, deep neural networks, DNN) to improve the decoding algorithms of short quasi-cyclic low-density paritycheck (LDPC) codes adopted to the 5G standard. We note that straightforward application of general-purpose DNNs is not possible due to the curse of dimensionality problem – the training set size grows exponentially with the number of information bits. In our opinion, the only way to deal with this problem is to combine deep learning methods with existing decoding algorithms. We start with a Tanner-based neural network decoder with Min-Sum activation functions proposed by Nachmani et al. and extend it as follows. First, the quasi-cyclic nature of 5G LDPC codes allows us to use a single weight per circular matrix (circulant). We refer to this as weight sharing. This idea significantly reduces the training time, preserving the error-correcting performance. Second, we add residual connections to our NN architecture. Residual connections improve the performance and reduce the training time. We also present the results for the rate and length adaptation techniques. Rate adaptation allows multiple DNNs corresponding to different coding rates to run with a single set of trained weights. Length adaptation allows optimally reusing weights for multiple lifting size indices.
The neural networks offer iteration capability for low-density parity-check (LDPC) decoding with superior performance at transmission. However, to cope with increasing code length and rate, the complexity of the neural network increases significantly. This is due to the large amount of feature extraction required to maintain the error correction capability. Based on this gap, we design a new iterative LDPC decoding technique named graph model neural network-belief propagation (GMNN-BP). GMNN-BP uses graph models as a link between deep learning and belief propagation (BP) algorithms, combining the advantages of both. Compared to traditional fully connected neural network decoders, the GMNN-BP decoding has the substantial benefit of avoiding learning and judging codeword categories directly from a large amount of data and requiring less training data as well. The proposed algorithm is verified by simulation and experiment and is tested by using IEEE 802.3ca standard LDPC code word. The results show that the GMNN-BP decoding algorithm is superior to the BP-based iterative decoding method under the same number of iterations, and the maximum gain can reach 1.9dB. When achieving the same performance, the GMNN-BP decoding algorithm only requires half the number of iterations of other algorithms.
In this work, we propose a neural adjusted min-sum (NAMS) decoder for low-density parity-check (LDPC) codes. In particular, we improve the traditional normalized min-sum (NMS) decoder by introducing a selection mechanism to adjust the check-node update step, where either the min-sum rule or the belief propagation (BP) rule is selected. Besides, we unfold the modified decoder into a model-driven neural network, where layer-dependent trainable parameters are introduced as weights in the Tanner graph and optimized by gradient descent-based methods during network training. Simulation results demonstrate that the proposed NAMS decoder is able to provide superior error-correction performance as compared to the neural NMS decoder, with only slightly increased computational complexity. Moreover, in certain circumstances, the proposed NAMS decoder even outperforms the neural BP decoder, with much lower computational complexity.
With changing scenarios in Beyond 5G (B5G) systems, channel coding methods will be faced with stronger requirements for reliability, flexibility, and low latency.Conventional decoding algorithms such as Belief Propagation (BP) are efficient in structured contexts but not sufficiently flexible to respond effectively to dynamic and noisy channel conditions.In this study, we introduces a new Graph Neural Network (GNN)-based solution to decode Low-Density Parity-Check (LDPC) codes by taking advantage of the intrinsic bipartite graph representation of Tanner graphs.The proposed decoder learns a data-driven messagepassing algorithm that performs better than BP over a large range of signal-to-noise ratios (SNRs) and block lengths.The experimental results show that the GNN-based decoder yields much lower bit error rates (BER), faster convergence, and better resistance to noise variability than belief propagation, especially at medium to high SNR levels.Thus, our findings highlight the foundation for scalable, adaptive, and intelligent decoding systems in B5G and 6G architectures.
LDPC codes, as an error correcting code close to the Shannon limit, are widely used in modern communication systems such as 5 G, satellite communication, deep space communication, and other fields. Traditional LDPC decoding algorithms, such as belief propagation (BP) algorithm and its variants, have achieved good performance, but face challenges such as high complexity and slow convergence, especially when dealing with long code lengths and high noise scenarios. The rise of deep learning has brought new opportunities for LDPC decoding, and its powerful features learning and pattern recognition capabilities are expected to break through the bottleneck of traditional decoding. Based on the overview of deep neural network decoding methods for LDPC codes by data-driven and model driven approaches, this paper analysis and comparison of error rate performance of short codeH(8,16)\mathbf{H} (8,16)H(8,16)matrix by convolutional neural networks (CNN), residual network (ResNet), and Kolmogorov-Arnold Network (KAN).